Anis Matoussi

Professor, Applied Mathematics at the University of Le Mans 
Head of Master "Mathematics for insurance, finance and health" (MAFS)
Co-Director of Risk and Insurance Institute of Le Mans
and Research Associate at CMAP-Ecole Polytechnique                                            


 University of Le Mans
 Risk and Insurance Institute of Le Mans 
 Laboratoire Manceau de Mathématiques 
 Avenue Olivier Messiaen 

 F-72085 Le Mans Cedex 9, France 
 Téléphone : + 33(0)2 43 83 37 19 
 Courrier électronique : anis.matoussi@

 - ANR CAESARS 2016-2019 (Control and simulAtion of Electrical Systems, interAction and RobustnesS), see website.

Research Interest

  • Backward Stochastic Differential Equations (BSDEs) :
    • Reflected BSDEs with one and two barriers.
    • Obstacle problem for Nonlinear PDEs.
    • Second order BSDEs.
  • Stochastic control applied to mathematical finance,  insurance and energy.  
    • Stochastic control under uncertainty.
    • Optimal allocation and investment. 
  • Stochastic nonlinear  PDEs
    • Maximum principle and obstacle problem for quasilinear SPDEs. 
    • Numerical computation and Monte Carlo methods.
    • Probabilistic representation for fully nonlinear SPDEs (classical and viscosity solution).

Recent Papers

35. N. El Karoui, A. Matoussi, A. Ngoupeyou. Quadratic Exponential  semimartingales and Applications to  BSDE with jumps. arXiv:1603.06191 (2016).

34. A. Matoussi, H. Xing. Convex Duality for stochastic  Differential Utility. arXiv :1601.03562v1 (2016), submitted.

33. A. Matoussi, D. Possamai, W. Sabbagh. Probabilistic Interpretation for Viscosity Solution of Fully Nonlinear SPDE's. arXiv :1412.5548 ( last version 2016), submitted.

32. M. Jeanblanc, A. Matoussi, A. Ngoupeyou. Robust utility maximization in a discontinuous filtration.  arXiv:1201.2690v2 (last version 2016), submitted

Accepted Papers

31. W. Faidi, A. Matoussi, M. Mnif. Robust utility maximization with a general penality term.  arXiv :1302.0442 (last version 2016),  to appear in  International Journal of Theoretical and Applied Finance (2017). 
30A. Matoussi, W. Sabbagh, T. Zhang. Backward doubly SDEs and semilinear SPDEs in a convex domain, arXiv:1405.5822v5 (last version 2016),  to appear in  Stochastic Processes and Their Applications (2017).
29. A. Matoussi, L. Piozin, A. Popier.  Stochastic PDEs with singular terminal condion, to appear in  Stochastic Processes and Their Applications (2017). 
28. A. Matoussi, W. Sabbagh. Numerical computation for backward doubly SDEs with random terminal time. Monte Carlo Methods Appl. 22, no. 3, 229–258 (2016).
27. A. Bachouch., E. Gobet, A. Matoussi.  Emperical Regression Method for Backward doubly SDEs, SIAM/ASA Journal on Uncertainty Quantification (JUQ), Vol. 4,  N°. 1, 358–379 (2016). 
26. A. Bachouch, M.-A. Ben Lasmar, A. Matoussi, M. Mnif. Euler time discretization of Backward Doubly SDEs and Applications to Semilinear SPDEs, Stochastic Partial Differential Equations : Analysis and Computations, 1, 1–43 (2016).                                    
25. Y. Hu, A. Matoussi, T. Zhang. Wong-Zakai approximation for Backward doubly SDEs. Stochastic  Processes and Their Applications, Vol. 125 (12), 4375-4404 (2015).       
24. A. Matoussi, H. Mezghani, M. Mnif. Maximization of recursive utilities under convex portfolio constraints.  Applied Mathematics and Optimization. Vol. 71 (2), 313-351 (2015). 
23A. Matoussi, D. Possamai and C. Zhou. Robust Utility Maximization in Non-dominated Models with 2BSDE : the Uncertain Volatility Model. Mathematical FinanceVol. 25, N°. 2, 258-287 (2015). 
22. L. Denis, A. Matoussi, J. Zhang. The Obstacle Problem for quasilinear SPDEs with non- homogeneous operator.  Discrete and Continuous Dynamical Systems Series A"(DCDS-A), Vol. 35,  N°. 11,  5185-5202 (2015). 
21. L. Denis, A. Matoussi, J. Zhang. The existence and uniqueness result for Quasilinear Stochastic PDEs with Obstacle under weaker integrability conditions. Stochastics and Dynamics, Vol. 15, N°.4, 1550023  (2015).
20A. Matoussi, W. Sabbagh, C. Zhou. The obstacle problem for semilinear parabolic partial integro-differential equations.  Stochastics and Dynamics Vol. 15, N°.1, 1550007 (2015).  
19.  L. Denis, A. Matoussi, J. Zhang. Maximum principle for quasilinear SPDEs with obstacle. Electronic  Journal of ProbabilityVol. 19, Issue 44, 1-32 (2014). 
18. A. Matoussi, L. Piozin, D. Possamai. Second-order BSDEs with general reflection and Dynkin games under uncertainty. Stochastic Processes and Their Applications, Vol. 124, Issue 7, 2281–2321 (2014).
17. L. Denis, A. Matoussi and J. Zhang. The Obstacle problem for quasilinear SPDEs : Analytical approach. The Annals of Probabilty, Vol. 42, No.3, 865–905 (2014). 
16. A. Matoussi,  D. Possamai  and C.  Zhou. Second order reflected backward stochastic differential equations. Ann. Appl. Probab. 23, no. 6, 2420–2457, (2013).
15. L. Denis, A. Matoussi. Maximum principle for quasilinear SPDE’s on a bounded domain without regularity assumptions. Stochastic Processes and Their Applications 123, 1104–1137 (2013).
14. W. Faidi, A. Matoussi, M. Mnif.  Maximization of Recursive Utilities: A Dynamic Maximum Principle Approach.  SIAM J. of Financial Math., Vol. 2, pp. 1014-1041 (2011). 
13. A. Matoussi,  L. Stoica. The Obstacle Problem for Quasilinear Stochastic PDE's. Annals of Probability, Vol. 38, N.3, 1143-1179 (2010).
12. L. Denis, A. Matoussi, L. Stoica. Moser iteration applied to parabolic SPDE’s: first approach. Quaderni di Matematica, Series edited by Dipartimento di Matematica     
Seconda Università di Napoli. Proceeding "Stochastic Partial Differential Equations and Applications – VIII" (Levico, Jan. 6-12, 2008), (2010). 
11. L. Denis,  A. Matoussi, L. Stoica. Maximum principle and comparison theorems for solutions of Quasilinear SPDE's. Electronic Journal of Probability 14, pp. 500-530 (2009).
10. S. Crépey, A. Matoussi. Reflected and Doubly Reflected BSDEs with jumpsAnnals of  Applied Probability 18, No. 5, pp. 2041-2069 (2008).
 9. A. Matoussi, M. Xu. Sobolev solution for semilinear PDE with obstacle under monotonocity condition. Electronic Journal of Probability  Vol. 13, No.35, 1035-1067 (2008).
 8. G. Bordigoni, A. Matoussi, M. Schweizer. A stochastic control approach to a robust utility maximization problem. Abel Symposium 2005. Stochastic Analysis and Applications, eds. F.E. Benth, G. Di Nunno, T. Lindstrom, B. Oksendal, T. Zhang. Springer-Verlag Berlin, pp. 125-151 (2007).
 7. L. Denis,  A. Matoussi, L. Stoica. Lp-estimates for the uniform norm of solutions quasilinear SPDE's.  Probability Theory and Related fields, 133, pp. 437-463 (2005).
 6. J.-P. Lepeltier, A. Matoussi, M. Xu. Reflected BSDE with monotonicity condition and general increasing growth conditionAdvances in Applied Probability 37, 134-159 (2005).
 5. S. Dereich, F. Fehringer, A. Matoussi and M. Scheutzow : On the link between small ball probabilities and the quantization problem for Gaussian measures on Banach spaces.  Journal of Theoretical Probability 16, 249-265 (2003).
 4. A. Matoussi, M. Scheutzow. Semilinear Stochastic PDE's with nonlinear noise and Backward Doubly SDE's.  Journal of Theoretical Probability 15, 1-39 (2002).
 3. V. Bally, A. Matoussi. Weak solutions of Stochastic PDEs and Backward doubly stochastic differential equationsJournal of Theoretical Probability 14, 125-164 (2001). 
 2. S. Hamadène, J.P. Lepeltier, A. Matoussi.  Double Barrier Reflected BSDEs with continuous coefficient. Backward stochastic differential equations. N. El Karoui and 
 L. Mazliak (Editors). Pitman Research Notes in Mathematics Series (1997).
 1. A. Matoussi. Reflected solutions of BSDEs with continuous coefficientStatistics and Probability Letters 34, 347-354 (1997).

Chapter in Books

N. EL Karoui, S. Hamadène, A. Matoussi.  Backward stochastic differential equations and applications. Chapter 8 in the book "Indifference Pricing: Theory and Applications" edited by René Carmona, Springer-Verlag  pp. 267-320 (2008).

Current PhD Students

- Arij MANAI (2015-), co-supervisor Habib Ouerdiane (University Tunis El Manar, Tunisia).

- Rym SALHI  (2015-), co-supervisor Habib Ouerdiane (University Tunis El Manar, Tunisia).

- Fanny Larissa NOUBIAGAIN Chomchie (2013- ), co-supervisor  Laurent Denis.

Former PhD Students

- Lambert PIOZIN (2011- 2015), currently junior Quant at HSBC London (UK).

- Anis BEN LASMAR (2010-2015),  currently Assistant Professor at ESPRIT (Engineers School), Tunis (Tunisia).

- Hanen MEZGHANI (2011-2015), currently Assistant Professor  at University of Gafsa (Tunisia).

- Wissal SABBAGH (2011-2014),  currently  Postdoc at University of Evry (France).

- Achref BACHOUCH (2010-2014), currently Postdoc at Humboldt University of Berlin (Germany).

- Jing ZHANG (2009-2012),  currently Assistant Professor  at Fudan University (Shanghai, Chine).  

- Wahid FAIDI (2008-2012),  currently Assistant Professor  at University of Tunis  El Manar (Tunisia).

- Chao ZHOU (2009-2012),  currently Assistant Professor  at National University of Singapore.

- Armand NGOUPEYOU (2007-2010),  currently  Risk manager at Central Bank of Africa (Cameroune).

- Hao WANG (2006-2009),  currently  Risk manager at Bank of China (Jinan, China)